Obliquity of Saturn: Numerical Model

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Obliquity of Saturn Numerical Model
Doug Hamilton and William Ward U. Maryland SwRI
Outline Jupiter Saturn Spin-Orbit
Coupling Numerical Simulations Conclusions
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Why Jupiter Saturn?

• Mercury, Venus Tidally despun. Spin axis
  orientations not primordial.
• Earth Obliquity from Moon-forming impact?
• Mars 0-60o oscillations in planet's tilt.
• Jupiter Obliquity not from giant impact?
• Saturn Obliquity not from giant impact?
• Uranus, Neptune Giant Impacts?
• Pluto Obliquity from moon-forming impact?

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Saturn Relevant Periods
Precession Period 1.83106 yr . g18 Secular
Period 1.87106 yr .
Coincidence?
Or perhaps Saturn is trapped in a Spin-Orbit
Resonance!

Neptune's Orbit contains 104 times more angular
momentum than Saturn's Spin.
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In the Early Solar System
Saturn's Precession Period Increased with Time
- Kelvin-Helmholtz Contraction of Saturn -
Depletion of Circumplanetary Satellite Disk The
g18 Secular Period Increased with Time
-Thinning of the Kuiper Belt -Outward Migration
of Neptune

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Numerical Simulations
Secular Planetary Theory of Bretagnon - 4 giant
planets - 1000's of planetary frequencies -
We use the 10 strongest secular terms (Von
Woerkom theory) Planetary Spin-Axis Evolution
from Ward -Second order in planetary
e,i Simple Models for Changes to Precession Rates

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Simple Trapping into Resonance
Obliquity reaches 27o.
Slow Depletion of the Kuiper Belt 5108 yrs.
Trapping occurs when period ratio is 1.0.
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Simple Trapping into Resonance
Polar Plot of the Resonant Angle.
Final libration is too Small!
Current Position of Saturn's Pole.
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Single Resonant Kick
Obliquity reaches 13o.
Resonant Kick
We impose this model (Slow Contraction of Saturn)
Kick occurs when period ratio is 1.0.
Integration Time on all plots is 4.5109 years.
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Kick Trapping Fastest Timescales
Obliquity reaches 27o.
KB Dissipates 1108 yrs.
Saturn Contracts 2.5107 yrs.
Trapping occurs when period ratio is 1.0.
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Kick Trapping Fastest Timescales
Final libration 40o.
Polar Plot of the Resonant Angle.
Current Position of Saturn's Pole.
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Models for Saturn's Obliquity
1. Giant Collision. Requires a Uranus-mass
object (-) 2. Entire Solar System tilted in
2Myr (Tremaine). 3. Secular Spin-Orbit
Resonance w/ Neptune. Strong nearby
resonance () Explains the value of the
obliquity () Consistant w/ current pole
position ()
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Results of this Study
1. New Understanding of the Origin of Saturn's
Obliquity. New Constraints Implied by
Jupiter's Low Obliquity. 2. Natural Explanation
for the Close Similarity of Saturn's
Precession and the g18 Periods. 3. Vindicates
the idea that Gas Accretion Produces Spin
Axes Nearly Perpendicular to Orbits. 4. New
Constraints on the Timescales of Early Solar
System Processes Affecting Saturn and
Neptune. 5. New Constraints on Early Solar
System Processes.